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The benefits of jointly managing the combined set of radio resources offered by heterogeneous networks consisting of several radio access technologies (RATs) have been profusely studied and assessed in recent years. This notion has been coined as common radio resource management (CRRM). Nevertheless, most of the existing work assumes scenarios where all RATs are accessible (provided the RAT is not at full capacity) to those users demanding a particular service. If this is so, the obtained benefits become rather optimistic given that we neglect the fact that the deployed RATs may have different coverage overlapping conditions among them and that users may not have terminals that support all RATs (i.e. multimode terminals). In this paper we extend a previously developed Markov framework in order to capture the effect of having different coverage overlapping conditions along with the capability of certain terminals to support all or a subset of available RATs. Probabilistic models are obtained for the characterization of a wide range of coverage and terminal heterogeneity scenarios. Extensive performance evaluation is carried out in order to identify those parameters influencing the suitability of a particular initial RAT selection strategy, that is, to choose the most suitable RAT at call/session initiation among those accessible. Results indicate that suitable RAT selection is tightly dependent on: the ratio between the different offered traffic loads (or service-mix), the contention (if any) for radio resources by different services in particular RATs, and the identification of access-constrained RATs due to lack of coverage and/or terminal capability. In this paper we provide specific guidelines and rules concerning resource allocation for the utmost utilization of radio resources, in terms of Erlang capacity, and enhanced perceived quality by the users, in terms of achievable throughput.