Context : In order to study the terrestrial-type planet formation during the post oligarchic growth , the initial distributions of planetary embryos and planetesimals used in N-body simulations play an important role .
In general , most of these studies typically use ad hoc initial distributions based primarily on theoretical and numerical studies .

Aims : We analyze the formation of planetary systems without gas giants around solar-type stars focusing on the sensitivity of the results to the particular initial distributions used for planetesimals and planetary embryos at the end of the gas phase of the protoplanetary disk .
The formation process of terrestrial planets in the habitable zone ( HZ ) and the study of their final water contents are also topics of special interest in this work .

Methods : We developed two different sets of N-body simulations starting with the same protoplanetary disk .
The first set assumes typical ad hoc initial distributions for embryos and planetesimals and the second set obtains these initial distributions from the results of a semi-analytical model which simulates the evolution of the protoplanetary disk during the gaseous phase .

Results : Both sets of simulations form planets within the HZ .
Using ad hoc initial conditions the masses of the planets that remain in the HZ range from 0.66 M _ { \oplus } to 2.27 M _ { \oplus } .
Using more realistic initial conditions obtained from a semi-analytical model , we found that the masses of the planets range from 1.18 M _ { \oplus } to 2.21 M _ { \oplus } .
Both sets of simulations form planets in the HZ with water contents ranging between 4.5 % and 39.48 % by mass .
Those planets that have the highest water contents with respect to those with the lowest water contents , present differences regarding the sources of water supply .

Conclusions : Comparing both sets of simulations we suggest that the number of planets that remain in the HZ is not sensitive to the particular initial distribution of embryos and planetesimals and thus , the results are globally similar between them .
However , the main differences observed between both sets are associated to the accretion history of the planets in the HZ .
These discrepancies have a direct impact in the accretion of water-rich material and in the physical characteristics of the resulting planets .