We present the results of the Hubble Space Telescope B –Band Parallel Survey ( BBPS ) . It covers 0.0370 square degrees and consists of 31 shallow ( 4–6 orbit ) , randomly selected high latitude HST WFPC2 parallel fields with images taken in both the B ( F450W ) and I ( F814W ) filters . The goal of this survey is to morphologically classify the galaxies in a homogeneous manner and study galaxy properties as a function of type and B –band magnitude for 18 \lesssim b _ { J } \lesssim 23.5 mag . The full sample contains 1800 galaxies , 370 of which are brighter than the formal statistical completeness limit of b _ { J } \lesssim 23.5 mag . The galaxies are selected from the B –band images and classified using an artificial neural network ( ANN ) galaxy classifier on the higher S/N I –band images . These provide ( more ) reliable types for I \lesssim 24 mag ( or { b _ { J } } \lesssim 26 mag ) , since these I –band classifications are less subject to the uncertain redshifted rest-frame UV morphology . The ANN classification depends on the shape of the surface brightness profile , but not on color . These results are combined with similar ( deeper ) studies in the Hubble Deep Field and the deep WFPC2 field surrounding the radio galaxy 53W002 , for which galaxies have been classified to b _ { J } \lesssim 27 mag . The galaxy counts for the combined B –band selected samples show adequate statistics for a range 19 \lesssim b _ { J } \lesssim 27 mag , and are in good agreement with other studies in the flux range where they overlap , while showing improved statistics at the bright end . The galaxies are subdivided into 3 morphological classes : early-types ( E/S0 ) , mid-types ( Sabc ) and late-types ( Sd/Irr ) , and the B –band counts are presented for each class , as well as the total counts . The faint end of the counts is dominated by the irregular galaxies , which have a steep count slope of d log N / dm \approx 0.4 . These type dependent counts are compared to models based on local luminosity functions which include the effects of the cosmological constant , \Omega _ { \Lambda } . The whole BBPS sample , along with the two deeper fields , is used to delineate the general trends of effective radius and ( B – I ) color as function of both morphological type and apparent magnitude for 18 \lesssim b _ { J } \lesssim 27 mag . These properties are discussed in the context of recent redshift surveys . A possible explanation for the combined results is given in terms of the effects of \Omega _ { \Lambda } on the evolution of the merger rate in a hierarchical scenario .