The molecular gas properties and circumnuclear star formation in the n
earby nuclear starburst galaxies NGC 2903, NGC 3351 and NGC 3504 are i
nvestigated in detail. The circumnuclear HII regions in the star-formi
ng rings of these galaxies are characterised by an ionized,gas mass in
the 10(4) - 10(5) M. range, and by an ionizing flux in the 10(51) -10
(52) ph s(-1) range, typical of giant HII regions in external galaxies
. The CO 2-->1 emission in NGC 3504 indicates the presence of two emit
ting regions separated by 115 km s(-1) in velocity and 5 '' (500 pc) s
patially, what approximately corresponds to the location of the the in
ner inner Lindblad resonance. The measured (CO 2-->1)/(CO 1-->0) integ
rated intensity ratio for the inner kpc of NGC 3351 is 0.8, in agreeme
nt with the empirical average value found for spiral galaxies with a n
ormal metallicity regardless of the presence or the absence of a starb
urst. Molecular gas masses in the range of M-H2 approximate to 10(8) -
10(9) M. are measured in regions of a few hundred parsecs in size. On
average, the circumnuclear region of the three galaxies is characteri
sed by an average molecular gas surface density Sigma(H2) = 280 M. pc(
-2), and average L-IR/M-H2 = 21 L. M.(-1). The L-IR/M-H2 - Sigma(H2) r
elationship covering the Sigma(H2) range from normal spiral galaxies a
nd giant molecular clouds in the Milky Way with Sigma(H2) similar to 1
0(1) - 10(2) M. pc(-2), to nearby starbursts, AGNs with starbursts, an
d luminous IRAS galaxies with Sigma(H2) similar to 2 10(2) - 10(5) M.
pc(-2), is investigated, Nearby starburst galaxies have an average mol
ecular gas surface density Sigma(H2) Of 400 M. pc(-2) and an average L
-IR/M-H2. Of 23 L. M.(-1).These two properties are explained by the ex
istence of giant molecular clouds with associated HII regions where th
e star formation process is characterised hv being short lived (less t
han or equal to 3 10(7) years), biased towards a high lower mass limit
M(i)ota similar to 3 M., and with an overall gas to stars conversion
fraction of less than or equal to 10% of the gas mass. The star format
ion efficiency (SFE) in nearby starbursts and luminous IRAS galaxies (
as measured by the L-IR/M-H2, ratio) does not show any indication of a
linear correlation with increasing Sigma(H3). On the contrary, the st
ar formation efficiency is restricted to the 10 < L-IR/M-H2 < 100 L.M.
(-1) range, and reaches a maximum value of L-IR/M-H2 = 100 L. M.(-1) f
or Sigma(H2) larger than 10(3) M. pc(-2). The upper limit found for th
e L-IR/M-H2 ratio, independent of Sigma(H2) implies the existence of a
n upper limit in the fraction of gas converted into stars independent
of the density. The SFE range observed in nearby starbursts, Seyferts
with starbursts, and luminous IRAS galaxies is explained as a combinat
ion of massive star formation in the circumnuclear regions of these ga
laxies plus the additional contribution of an AGN at the center of the
galaxy. Under the starburst + AGN scenario, most of the molecular gas
mass is directly involved in the star forming process while the AGN c
ontribution to the global IR luminosity is in the 10% to 75% range, de
pending on the galaxy. In this scenario, the infrared luminosity of ga
laxies with observed L-IR/M-H2, ratio in the 10 to 30 L. M.(-1) range
is dominated by the circumnuclear star formation alone. The infrared l
uminosity in those galaxies with L-IR/M-H2, in the 30 - 100 L. M.(-1)
range is increasingly dominated by the central AGN. Examples of this s
ituation are NGC 1068, NGC 7469 and Mrk 231.